Data communication typically occurs as the transfer of information from one communication device to another. This is typically accomplished by the use of a modem located at each communication endpoint. In the past, the term modem denoted a piece of communication apparatus that performed a modulation and demodulation function, hence the term “modem”. Today, the term modem is typically used to denote any piece of communication apparatus that enables the transfer of data and voice information from one location to another. For example, modem communication systems use many different technologies to perform the transfer of information from one location to another. Digital subscriber line (DSL) technology is one vehicle for such transfer of information. DSL technology uses the widely available subscriber loop, the copper wire pair that extends from a telephone company central office to a residential location, over which communication services, including the exchange of voice and data, may be provisioned. DSL devices can be referred to as modems, or, more accurately, transceivers, which connect the telephone company central office (CO) to the user, or remote location, typically referred to as the customer premises (CP). DSL communication devices use different formats and different types of modulation schemes and achieve widely varying communication rates. However, even the slowest DSL communications devices achieve data rates far in excess of conventional point-to-point modems.
Some of the available modulation schemes include quadrature-amplitude modulation (QAM), carrierless amplitude/phase (CAP) and discrete multi-tone (DMT). Early QAM modems and all CAP and DMT transceivers use square signal constellations, which are relatively simple to implement, but which suffer from 0.2 dB performance loss and a high 6 dB peak factor. Peak factor refers to the highest power level associated with any point in the signal constellation. High peak factor leads to higher energy required to transmit those square signal constellations.
To improve the performance and lower the peak factor, circular signal constellations were introduced. Circular signal constellations have improved performance and lower overall peak factor than square signal constellations. Efficient coding tables are available for generating the constellations for 10 to 12 bit-per-symbol constellations. Coding tables are look-up tables that relate each point in a signal constellation to an associated vector. The vector represents the phase and amplitude of the particular signal point represented in a two-dimensional arrangement. Unfortunately, at bit-per-symbol densities higher than 12 bits, the coding tables become quite large and unmanageable. For example, for a 15 bit per symbol circular constellation, the coding table includes 27,806 code words. This would require an extraordinarily large amount of memory and consume valuable microprocessor time to implement.
This situation is unfortunate because the copper wire pairs over which DSL transceivers operate are capable of supporting extremely high data rates, allowing the transmission of 15 bits-per-symbol or greater.
Therefore, it would be desirable to provide a way of communicating high bit-per-symbol circular signal constellations without the need for implementing unduly large look-up tables and without the need for implementing the high-powered line drivers required for communicating high peak factor square signal constellations.